diff options
Diffstat (limited to 'moon-abe/pbc-0.5.14/ecc/singular.c')
| -rw-r--r-- | moon-abe/pbc-0.5.14/ecc/singular.c | 447 |
1 files changed, 0 insertions, 447 deletions
diff --git a/moon-abe/pbc-0.5.14/ecc/singular.c b/moon-abe/pbc-0.5.14/ecc/singular.c deleted file mode 100644 index 95f00410..00000000 --- a/moon-abe/pbc-0.5.14/ecc/singular.c +++ /dev/null @@ -1,447 +0,0 @@ -#include <stdarg.h> -#include <stdio.h> -#include <stdint.h> // for intptr_t -#include <stdlib.h> -#include <gmp.h> -#include "pbc_utils.h" -#include "pbc_field.h" -#include "pbc_curve.h" -#include "pbc_param.h" -#include "pbc_pairing.h" -#include "pbc_fp.h" -#include "pbc_memory.h" - -//TODO: Store as integer mod ring instead and convert at last minute? -struct point_s { - int inf_flag; - element_t x; - element_t y; -}; -typedef struct point_s *point_ptr; -typedef struct point_s point_t[1]; - -static void sn_init(element_ptr e) { - field_ptr f = e->field->data; - e->data = pbc_malloc(sizeof(point_t)); - point_ptr p = e->data; - element_init(p->x, f); - element_init(p->y, f); - p->inf_flag = 1; -} - -static void sn_clear(element_ptr e) { - point_ptr p = e->data; - element_clear(p->x); - element_clear(p->y); - pbc_free(e->data); -} - -static void sn_set0(element_ptr x) { - point_ptr p = x->data; - p->inf_flag = 1; -} - -static int sn_is0(element_ptr x) { - point_ptr p = x->data; - return p->inf_flag; -} - -//singular with node: y^2 = x^3 + x^2 -static void sn_random(element_t a) { - point_ptr p = a->data; - element_t t; - - element_init(t, p->x->field); - p->inf_flag = 0; - do { - element_random(p->x); - if (element_is0(p->x)) continue; - element_square(t, p->x); - element_add(t, t, p->x); - element_mul(t, t, p->x); - } while (!element_is_sqr(t)); - element_sqrt(p->y, t); - - element_clear(t); -} - -static inline void sn_double_no_check(point_ptr r, point_ptr p) { - element_t lambda, e0, e1; - - element_init(lambda, p->x->field); - element_init(e0, p->x->field); - element_init(e1, p->x->field); - //same point: double them - - //lambda = (3x^2 + 2x) / 2y - element_mul_si(lambda, p->x, 3); - element_set_si(e0, 2); - element_add(lambda, lambda, e0); - element_mul(lambda, lambda, p->x); - element_add(e0, p->y, p->y); - element_invert(e0, e0); - element_mul(lambda, lambda, e0); - //x1 = lambda^2 - 2x - 1 - element_add(e1, p->x, p->x); - element_square(e0, lambda); - element_sub(e0, e0, e1); - element_set_si(e1, 1); - element_sub(e0, e0, e1); - //y1 = (x - x1)lambda - y - element_sub(e1, p->x, e0); - element_mul(e1, e1, lambda); - element_sub(e1, e1, p->y); - - element_set(r->x, e0); - element_set(r->y, e1); - r->inf_flag = 0; - - element_clear(lambda); - element_clear(e0); - element_clear(e1); - return; -} - -static void sn_double(element_t c, element_t a) { - point_ptr r = c->data; - point_ptr p = a->data; - if (p->inf_flag) { - r->inf_flag = 1; - return; - } - if (element_is0(p->y)) { - r->inf_flag = 1; - return; - } - sn_double_no_check(r, p); -} - -static void sn_set(element_ptr c, element_ptr a) { - point_ptr r = c->data, p = a->data; - if (p->inf_flag) { - r->inf_flag = 1; - return; - } - r->inf_flag = 0; - element_set(r->x, p->x); - element_set(r->y, p->y); -} - -static void sn_add(element_t c, element_t a, element_t b) { - point_ptr r = c->data; - point_ptr p = a->data; - point_ptr q = b->data; - if (p->inf_flag) { - sn_set(c, b); - return; - } - if (q->inf_flag) { - sn_set(c, a); - return; - } - if (!element_cmp(p->x, q->x)) { - if (!element_cmp(p->y, q->y)) { - if (element_is0(p->y)) { - r->inf_flag = 1; - return; - } else { - sn_double_no_check(r, p); - return; - } - } - //points are inverses of each other - r->inf_flag = 1; - return; - } else { - element_t lambda, e0, e1; - - element_init(lambda, p->x->field); - element_init(e0, p->x->field); - element_init(e1, p->x->field); - - //lambda = (y2-y1)/(x2-x1) - element_sub(e0, q->x, p->x); - element_invert(e0, e0); - element_sub(lambda, q->y, p->y); - element_mul(lambda, lambda, e0); - //x3 = lambda^2 - x1 - x2 - 1 - element_square(e0, lambda); - element_sub(e0, e0, p->x); - element_sub(e0, e0, q->x); - element_set1(e1); - element_sub(e0, e0, e1); - //y3 = (x1-x3)lambda - y1 - element_sub(e1, p->x, e0); - element_mul(e1, e1, lambda); - element_sub(e1, e1, p->y); - - element_set(r->x, e0); - element_set(r->y, e1); - r->inf_flag = 0; - - element_clear(lambda); - element_clear(e0); - element_clear(e1); - } -} - -static void sn_invert(element_ptr c, element_ptr a) { - point_ptr r = c->data, p = a->data; - - if (p->inf_flag) { - r->inf_flag = 1; - return; - } - r->inf_flag = 0; - element_set(r->x, p->x); - element_neg(r->y, p->y); -} - -static void sn_field_clear(field_ptr c) { - UNUSED_VAR(c); -} - -/* TODO: Write a test program that uses these functions. - -// Nonsingular points on sn curves map to finite field elements via -// (x, y) --> (y + x)/(y - x) -// The reverse map is -// a --> (4a/(a-1)^2, 4a(a+1)/(a-1)^3) - -void sn_point_to_field(element_t out, point_ptr P) { - element_t e0, e1; - if (P->inf_flag) { - element_set1(out); - return; - } - element_init(e0, out->field); - element_init(e1, out->field); - element_add(e0, P->y, P->x); - element_sub(e1, P->y, P->x); - element_invert(e1, e1); - element_mul(out, e0, e1); - element_clear(e0); - element_clear(e1); -} - -static void sn_field_to_point(point_ptr P, element_t in) { - element_t e0, e1, e2; - - if (element_is1(in)) { - P->inf_flag = 1; - return; - } - element_init(e0, in->field); - element_init(e1, in->field); - element_init(e2, in->field); - - element_set1(e1); - element_sub(e0, in, e1); - element_invert(e0, e0); - - element_mul_si(e2, in, 4); - - element_add(P->y, in, e1); - - element_mul(e1, e0, e0); - element_mul(P->x, e1, e2); - element_mul(P->y, P->y, e2); - element_mul(P->y, P->y, e0); - element_mul(P->y, P->y, e1); - P->inf_flag = 0; - - element_clear(e0); - element_clear(e1); - element_clear(e2); -} -*/ - -static size_t sn_out_str(FILE *stream, int base, element_ptr a) { - point_ptr p = a->data; - size_t result, status; - if (p->inf_flag) { - if (EOF == fputc('O', stream)) return 0; - return 1; - } - result = element_out_str(stream, base, p->x); - if (!result) return 0; - if (EOF == fputc(' ', stream)) return 0; - status = element_out_str(stream, base, p->y); - if (!status) return 0; - return result + status + 1; -} - -void naive_generic_pow_mpz(element_ptr x, element_ptr a, mpz_ptr n); -void field_init_curve_singular_with_node(field_t c, field_t field) { - mpz_set(c->order, field->order); - c->data = (void *) field; - c->init = sn_init; - c->clear = sn_clear; - c->random = sn_random; - //c->from_x = cc_from_x; - //c->from_hash = cc_from_hash; - c->set = sn_set; - c->invert = c->neg = sn_invert; - c->square = c->doub = sn_double; - c->mul = c->add = sn_add; - c->set1 = c->set0 = sn_set0; - c->is1 = c->is0 = sn_is0; - c->mul_mpz = element_pow_mpz; - c->out_str = sn_out_str; - c->field_clear = sn_field_clear; -} - -//TODO: the following code is useless as the Tate pairing is degenerate on singular curves -static void sn_miller(element_t res, mpz_t q, element_t P, - element_ptr Qx, element_ptr Qy) { - //collate divisions - int m; - element_t v, vd; - element_t Z; - element_t a, b, c; - element_t e0, e1; - element_ptr Zx; - element_ptr Zy; - const element_ptr Px = curve_x_coord(P); - const element_ptr Py = curve_y_coord(P); - - #define do_vertical(e) \ - element_sub(e0, Qx, Zx); \ - element_mul(e, e, e0); - - //a = -slope_tangent(Z.x, Z.y); - //b = 1; - //c = -(Z.y + a * Z.x); - //but we multiply by 2*Z.y to avoid division - //a = -Zx * (Zx + Zx + Zx + 2) - //b = 2 * Zy - //c = -(2 Zy^2 + a Zx); - #define do_tangent(e) \ - element_double(e0, Zx); \ - element_add(a, Zx, e0); \ - element_set_si(e0, 2); \ - element_add(a, a, e0); \ - element_mul(a, a, Zx); \ - element_neg(a, a); \ - element_add(b, Zy, Zy); \ - element_mul(e0, b, Zy); \ - element_mul(c, a, Zx); \ - element_add(c, c, e0); \ - element_neg(c, c); \ - element_mul(e0, a, Qx); \ - element_mul(e1, b, Qy); \ - element_add(e0, e0, e1); \ - element_add(e0, e0, c); \ - element_mul(e, e, e0); - - //a = -(B.y - A.y) / (B.x - A.x); - //b = 1; - //c = -(A.y + a * A.x); - //but we'll multiply by B.x - A.x to avoid division - #define do_line(e) \ - element_sub(b, Px, Zx); \ - element_sub(a, Zy, Py); \ - element_mul(e0, b, Zy); \ - element_mul(c, a, Zx); \ - element_add(c, c, e0); \ - element_neg(c, c); \ - element_mul(e0, a, Qx); \ - element_mul(e1, b, Qy); \ - element_add(e0, e0, e1); \ - element_add(e0, e0, c); \ - element_mul(e, e, e0); - - element_init(a, Px->field); - element_init(b, Px->field); - element_init(c, Px->field); - element_init(e0, res->field); - element_init(e1, res->field); - - element_init(v, res->field); - element_init(vd, res->field); - element_init(Z, P->field); - - element_set(Z, P); - Zx = curve_x_coord(Z); - Zy = curve_y_coord(Z); - - element_set1(v); - element_set1(vd); - m = mpz_sizeinbase(q, 2) - 2; - - while(m >= 0) { - element_mul(v, v, v); - element_mul(vd, vd, vd); - do_tangent(v); - element_double(Z, Z); - do_vertical(vd); - if (mpz_tstbit(q, m)) { - do_line(v); - element_add(Z, Z, P); - do_vertical(vd); - } - m--; - } - #undef do_tangent - #undef do_vertical - #undef do_line - - element_invert(vd, vd); - element_mul(res, v, vd); - - element_clear(v); - element_clear(vd); - element_clear(Z); - element_clear(a); - element_clear(b); - element_clear(c); - element_clear(e0); - element_clear(e1); -} - -struct sn_pairing_data_s { - field_t Fq, Eq; -}; -typedef struct sn_pairing_data_s sn_pairing_data_t[1]; -typedef struct sn_pairing_data_s *sn_pairing_data_ptr; - -static void sn_pairing(element_ptr out, element_ptr in1, element_ptr in2, - pairing_t pairing) { - sn_pairing_data_ptr p = pairing->data; - element_ptr Q = in2; - element_t e0; - element_t R, QR; - element_init(R, p->Eq); - element_init(QR, p->Eq); - element_random(R); - element_init(e0, out->field); - element_add(QR, Q, R); - sn_miller(out, pairing->r, in1, curve_x_coord(QR), curve_y_coord(QR)); - sn_miller(e0, pairing->r, in1, curve_x_coord(R), curve_y_coord(R)); - element_invert(e0, e0); - element_mul(out, out, e0); - //element_pow_mpz(out, out, p->tateexp); - element_clear(R); - element_clear(QR); -} - -void pairing_init_singular_with_node(pairing_t pairing, mpz_t q) { - sn_pairing_data_ptr p; - - mpz_init(pairing->r); - mpz_sub_ui(pairing->r, q, 1); - field_init_fp(pairing->Zr, pairing->r); - pairing->map = sn_pairing; - - p = pairing->data = pbc_malloc(sizeof(sn_pairing_data_t)); - field_init_fp(p->Fq, q); - field_init_curve_singular_with_node(p->Eq, p->Fq); - - //mpz_init(p->tateexp); - //mpz_sub_ui(p->tateexp, p->Fq->order, 1); - //mpz_divexact(p->tateexp, p->tateexp, pairing->r); - - pairing->G2 = pairing->G1 = p->Eq; - - pairing_GT_init(pairing, p->Fq); -} |